2 Answers
2

From my experience with the Software Center and the Humble Indie Bundle apps, no, they will not be charged again. I've installed updates to Bastion without any re-payment, though I redeemed the Bundle apps via the gift codes, so it might be different for store-bought apps.

Technical

When you purchase an app, it adds a private repository (a.k.a. PPA, or personal package archive) to the folder /etc/apt/sources.list.d, e.g. private-ppa.launchpad.net_commercial-ppa-uploaders_bastion_ubuntu.list. The URL inside the file does not change when the app is updated, so I assume you will never have to re-purchase as long as the app is not republished under a new name.